In medium bowl, stir shredded apple with poultry seasoning, 1/2 teaspoon salt, and 1/4 teaspoon ground black pepper until blended. Mix in chicken and celery just until combined, but do not overmix. Shape chicken mixture into four 1/2-inch-thick burgers, handling mixture as little as possible.

Place burgers in grill pan; cook 10 to 12 minutes or just until chicken loses its pink color throughout, turning over once. Serve burgers on buns with apple rings and cranberry sauce.